Solve the Problem $y = \ln x$ , The $x$ -Axis, and the Vertical Line

question 432

Multiple Choice

Solve the problem.
-Find the volume of the solid generated by revolving the region bounded by the curve $y = \ln x$ , the $x$ -axis, and the vertical line $x = e ^ { 2 }$ about the $x$ -axis.

• A) \(\pi \left( e ^ { 2 } - 1 \right)\)
• B) \(\pi ( e - 1 )\)
• C) \(2 \pi \left( \mathrm { e } ^ { 2 } - 1 \right)\)
• D) \(\pi \mathrm { e }\)

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Definitions:

Rawlsian Justice

A theory of justice developed by John Rawls that emphasizes equal basic rights, equality of opportunity, and the promotion of the interests of the least advantaged members of society.

Social Contract

A theory or model that explains the origin of society and government as an implicit agreement among individuals to ensure collective security and welfare.

Distributional Justice

The ethical consideration of the fairness in the spread of wealth, income, and resources among all members of society.

Rawlsian Justice

A theory of justice that emphasizes fairness and equality, proposing that social and economic inequalities should be arranged to benefit the least advantaged members of society.